Question

Estimate the time for homogenised juice pulp particles to settle in juice concentrate through a distance of 1.5 m.
The pulp particles can be assumed spherical with a mean diameter of 0.5 mm and density of 1400 kg/3.
The juice concentrate has a density of 1300 kg/m3 and viscosity of 50 cp

Answer 1

This question is not of kinematics and gravitational mechanics. If we see, the density of body and fluis is very close which shows that the body will take much more time to fall 1.5m.

Lets first find terminal velocity for a spherical body  

v = 2/9 *{π.r^2.g( ρ - σ)}/η
where,
v = terminal velocity
r = radius of spherical body
g = acceleration due to gravity
ρ = density of spherical body
σ = density of liquid
η = coefficient of viscosity = 50 cP = .05 kg·m⁻¹·s⁻¹

so V= .00349 m/s

so we see that the velocity is very small and will be quickly attained by the spherical body, after that the body will move down with a constant velocity of .00349 m/s

So time taken to fall 1.5 m = 1.5/v = 1.5/.00349= 430 seconds = 7 minutes 10 sec.

Hope the answer was clear. Please like and give feedback.

Thanks